37 - Inner Product

Inner Product

Let $V$ be a real vector space $V$
An inner product is a positive definite, symmetric bilinear form on $V$

It is typically denoted as $⟨x,y⟩$ rather than $B(x,y)$

Note that $⟨-,-⟩$ will denote an inner product

Inner Product Space

A real vector space equipped with an inner product

Examples of Inner Products

1. Dot Product
2. Vector space of polynomials where

$$⟨f,g⟩={\int }_a^{b}f(x)g(x)dx$$